Question

Given that tan `2pi//9=0.8391`, use equivalent trigonometric expressions to evaluate cot `5pi//18`, to four decimal places?

Answer 1

`cot((5pi)/18)=0.8391`

Explanation:

`tan((2pi)/9)=0.8391`

`cot(pi/2 - Theta)=tan(Theta)`
`:.`
`cot((5pi)/18)=cot(pi/2 - (2pi)/9)=tan((2pi)/9)=0.8391`

Answer 2

`0.8391`

Explanation:

`cot((5pi)/18)=cot((2pi)/9+pi/18)`

`color(green)(tan(a+b)=(tana+tanb)/(1-tana*tanb)`

`=1/(tan((2pi)/9+pi/18))=(1-tan((2pi)/9)*tan(pi/18))/(tan((2pi)/9)+tan(pi/18)`

`tan(pi/18)=0.17633`

`=(1-0.8391*0.17633)/(0.8391+0.17633)=0.8391`